Last Stage Blade Design to Reduce Turndown Vibration

ABSTRACT

A turbine bucket includes a bucket airfoil having a cross-section in an airfoil shape. The bucket is twisted from a root end to a tip end. A degree of twist defines an accumulated angular offset of the tip end in a range of 10-15° relative to a tangential direction, thereby reducing excess negative incidence by 15-20° relative to the tangential direction.

BACKGROUND OF THE INVENTION

The invention relates generally to turbines and, more particularly, tolast stage blades of steam turbines.

Last stage blades or “buckets” (LSBs) of steam turbines are designedwith tip sections resembling flat plates. The orientation of the tipsection is more or less closely aligned, depending on rotational speedand radius ratio, with the tangential direction to match the directionof the flow at outer flow filament radial locations. The preciseorientation of the tip section is determined by flow analysis, at ornear the design point. However, steam turbines are required to operateat very low flows and high exhaust pressures relative to the designpoint, to accommodate load demand and atmospheric conditions,respectively. This causes significant deviation in the flow directionand velocity at the bucket tip, resulting in flow induced vibration(FIV), which is potentially damaging and limits operational flexibilityonce a threshold value of negative incidence is exceeded.

FIG. 2 shows a typical steam turbine last stage geometry at the tip,with flow velocity vectors, and FIG. 3 shows a more detailed view of alast stage blade section viewed radially inward from the tip. At steamturbine turndown conditions associated with light load and/or highexhaust pressure, the flow at the blade or bucket tip deviatessignificantly from the design point in both magnitude and direction. Themagnitude increases and in the limit of no flow reaches that of thewheelspeed vector W while the direction shifts from design optimumentrance angle toward the tangential direction opposite to bladerotation. If the turndown is significant, the flow incidence, defined asthe difference in optimum entrance angle and the actual flow direction,can exceed 15 degrees and result in elevated FIV, associated withairfoil concave or pressure side flow separation and stall.

FIG. 4 is a graph of blade or bucket tip flow incidence vs. average flowvelocity (Van) in the exit annulus. The graph indicates that at about 15degrees of incidence, the FIV, flutter, or more specifically stallflutter, is initiated, provided structural damping is low. Stall fluttercan result in short term failure of blades. Operating guidelines toavoid the turndown regime in which it may occur are a standard practicefor the industry. A somewhat more benign FIV behavior, buffeting aka“random resonant response” can occur at the same incidence threshold andhas been associated with blade failures and/or blade connection failuresover longer periods of operation.

It would be desirable to minimize FIV at turndown conditions, which canbe achieved by modifying the tip design for the applicable range ofradius ratios and speeds.

BRIEF DESCRIPTION OF THE INVENTION

A turbine bucket includes a bucket airfoil having a cross-section in anairfoil shape. The bucket is twisted from a root end to a tip end. Adegree of twist defines an accumulated angular offset of the tip end ina range of 10-15° relative to a tangential direction, thereby reducingexcess negative incidence by 15-20° relative to the tangentialdirection.

In another exemplary embodiment, a turbine includes a rotor, a rotatableshaft that rotates with the rotor, and a turbine coupled with therotatable shaft and the rotor. The turbine includes a plurality ofaxially spaced rotor wheels. A plurality of buckets are coupled witheach rotor wheel, where each of the buckets has a cross-section in anairfoil shape. A last stage bucket is twisted from a root end to a tipend, and a degree of twist defines an accumulated angular offset of thetip end in a range of 10-15° relative to a tangential direction, therebyreducing excess negative incidence by 15-20° relative to the tangentialdirection.

In yet another exemplary embodiment, a method of reducing flow inducedvibration in a last stage turbine bucket includes the step of twistingthe turbine bucket to a degree that defines an accumulated angularoffset of the tip end in a range of 10-15° relative to a tangentialdirection, thereby reducing excess negative incidence by 15-20° relativeto the tangential direction.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a perspective partial cut-away illustration of a low pressuresection of a condensing steam turbine, i.e. a steam turbine section thathas a sub-atmospheric exhaust pressure;

FIG. 2 shows a typical steam turbine last stage geometry at the tip,indicating design and off-design bucket tip entrance velocities;

FIG. 3 shows a detailed view of a last stage blade section viewedradially inward from the tip;

FIG. 4 is a graph of blade tip flow incidence versus average flowvelocity in the exit annulus; and

FIGS. 5 and 6 compare a last stage bucket existing design (FIG. 5) withthe last stage bucket design of the described embodiments (FIG. 6).

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a perspective partial cut away view of a low pressure (LP)steam turbine section 10 including a rotor 12 that includes a shaft 14and a last stage bucket (LSB) row 16. The LP turbine 10 includes aplurality of axially spaced rotor wheels 18. A plurality of buckets 20are mechanically coupled to each rotor wheel 18. More specifically, thebuckets 20 are arranged in rows that extend circumferentially aroundeach rotor wheel 18. A plurality of stationary nozzles 22 extendcircumferentially around the rotor 12 and are axially positioned betweenadjacent rows of the buckets 20. Nozzles 22 cooperate with the buckets20 to form a turbine stage and to define a portion of a steam flow paththrough the turbine 10.

In operation, steam 24 enters an inlet 26 of the turbine 10 and ischanneled through the nozzles 22. The nozzles 22 direct the steam 24downstream against the buckets 20. The steam 24 passes through theremaining stages imparting a force on the buckets 20 causing the rotor12 to rotate. At least one end of the turbine 10 may extend axially awayfrom the rotor 12 and may be attached to a load or machinery (notshown), such as, but not limited to, a generator, and/or anotherturbine. Accordingly, a large steam turbine unit may actually includeseveral low pressure turbines that are all co-axially coupled to thesame shaft 14. Such a unit may, for example, include a high-pressureturbine coupled to an intermediate-pressure turbine, which is coupled toa low-pressure turbine.

The significance of the turndown FIV region is that at conditions of lowflow and high exhaust pressure, the flow through the LSB passageseparates at the hub and is confined to a filament between approximately80 and 100% of the radial height (where radial height is defined as 0%at a root end 201 of the bucket and 100% at a tip end 202 of thebucket). Thus it is primarily in this region that turndown FIV flowincidence has meaning. The limiting flow angle is the highest value offlow angle that can be achieved. In order for significant FIV to occur,the difference between the LSB tip optimum entrance angle (OEA),frequently taken as the mean of the distribution over the last 20% ofradial height, and 180 degrees must exceed 15 degrees, negative. Thus,an LSB design with a tip OEA of 165 or more should not experienceturndown FIV. The 40″ LSB for 3600 rpm applications closely approachesthis criterion, while the 33.5″, 30″ and 26″, at the same rotationalspeed with progressively more excess negative incidence, have increasingpotential for FIV at turndown. Data acquired in the field with straingages demonstrates conclusively that the 30″ LSB vibration amplitudesare significantly greater than those of the 33.5″ at similar conditionsof turndown operation thus tending to confirm this theory.

Above approximately 40″ radial height, for 3600 rpm designs, it isgenerally expected that the required 15 degrees of negative incidencecannot be achieved for buckets designed by state of the art aerodynamicdesign methods, as such LSBs will have tip OEAs greater than 165degrees. The same statement is true for full and half speed buckets withactive lengths scalable from 3600 rpm designs on the basis of speed. Forexample, at 3000 rpm a bucket with radial height=(3600/3000)×35″=42″should also be low in turndown FIV potential.

FIGS. 5 and 6 show an existing 30″ design (FIG. 5) and a 30″ design(FIG. 6) reflecting the concepts of the proposed design. The proposeddesign increases the twist of the vane in sections between 30% and 60%height range, resulting in an accumulated angular offset of the tipsection on the order of 13 degrees. This is consistent with a reductionof excess negative incidence by 17 degrees, greatly reducing FIVpotential. An alternative way to achieve the same result of reorientingthe tip may be to incorporate the required twist in sections closer tothe root and provide relatively little section to section twist near thetip. A performance analysis could accompany any final design todetermine the best distribution of optimum entrance angle for designpoint performance, while ensuring that the goal of minimum excessnegative incidence at the tip is achieved. The end result would be anLSB design with a tip orientation as shown in FIG. 6. In addition tooptimizing the optimum entrance angle distribution to meet performanceand FIV reduction objectives, the leading edge of the blade can beradiused to reduce positive incidence performance sensitivity.

The design is applicable to LSB designs incorporating pin and finger,dovetails, curved or straight axial entry dovetails or dovetails of thetangential entry type, the latter including a radial notch in the wheelto permit assembly, and a pinned block or notch blade to completely fillthe wheel. The design is applicable to LSBs that are of the“freestanding” type (i.e., no connections between adjacent airfoils), aswell as LSBs with midspan and/or tip shroud connections. Additionally,the last stage nozzle may remain the same as a design with a LSB ofconventional section twist from root to tip, or have adjusted throatopenings starting at a location reasonably removed (˜25%) from the rootto preserve low root reaction. The adjustment should be such to ensurethat the LSB entrance flow angle is as close as possible to the LSBmetal section preferred entrance angle at all radial locations.Alternately an entirely redesigned nozzle may be applied. The adjustmentor redesigned nozzle will ensure the highest possible stage performance.The LSB design approach described herein can be applied to conventionalas well as high exhaust pressure designs, the latter having much higherexhaust pressure limits required for steam turbines in power plants withan air cooled condenser operating in high ambient temperatureconditions.

The described embodiments serve to reduce flow induced forces that causeoff-design vibration, by airfoil redesign. The airfoil tip section isdesigned so that stalled flow is greatly mitigated at turndownconditions. Particularly, this is accomplished by specifying a tipsection inclination relative to the tangential direction at a specifiedangle. As a result, a safe operating range is increased, providingcustomers with more freedom and responding to load demand, particularlyin hot weather. Additionally, last stage bucket reliability isincreased, particularly in cases where the customer operates the turbinebeyond manufacturer recommended limits.

While the invention has been described in connection with what ispresently considered to be the most practical and preferred embodiments,it is to be understood that the invention is not to be limited to thedisclosed embodiments, but on the contrary, is intended to cover variousmodifications and equivalent arrangements included within the spirit andscope of the appended claims.

What is claimed is:
 1. A turbine bucket including a bucket airfoilhaving a cross-section in an airfoil shape, the turbine bucket beingtwisted from a root end to a tip end, wherein a degree of twist definesan accumulated angular offset of the tip end in a range of 10-15°relative to a tangential direction, thereby reducing excess negativeincidence by 15-20° relative to the tangential direction.
 2. A turbinebucket according to claim 1, wherein the degree of twist defines anaccumulated angular offset of the tip end of 13°, thereby reducingexcess negative incidence by 17°.
 3. A turbine bucket according to claim1, comprising a leading edge, the leading edge being radiused to reducepositive incidence performance sensitivity.
 4. A turbine bucketaccording to claim 1, wherein a height dimension is defined as 0% heightat the root end and 100% height at the tip end, and wherein the turbinebucket is twisted in a section between 30-60% height to a degree that ishigher than other sections of the turbine bucket.
 5. A turbine bucketaccording to claim 1, wherein the turbine bucket is twisted at the rootend to a degree that is higher than other sections of the turbinebucket.
 6. A turbine bucket according to claim 1, wherein the turbinebucket is a last stage bucket of a turbine.
 7. A turbine bucketaccording to claim 6, wherein at an operating speed of 3,600 RPMs, amaximum height of the turbine bucket is 35 inches.
 8. A turbine bucketaccording to claim 6, wherein at an operating speed of X RPMs, a maximumheight of the turbine bucket is 3600/X*35.
 9. A turbine comprising: arotor; a rotatable shaft that rotates with the rotor; and a turbinecoupled with the rotatable shaft and the rotor, the turbine including aplurality of axially spaced rotor wheels, wherein a plurality of bucketsare coupled with each rotor wheel, each of the buckets having across-section in an airfoil shape, wherein a last stage bucket istwisted from a root end to a tip end, and wherein a degree of twistdefines an accumulated angular offset of the tip end in a range of10-15° relative to a tangential direction, thereby reducing excessnegative incidence by 15-20° relative to the tangential direction.
 10. Aturbine according to claim 9, wherein the degree of twist defines anaccumulated angular offset of the tip end of 13°, thereby reducingexcess negative incidence by 17°.
 11. A turbine according to claim 9,wherein the last stage bucket comprises a leading edge, the leading edgebeing radiused to reduce positive incidence performance sensitivity. 12.A turbine according to claim 9, wherein a height dimension of the laststage bucket is defined as 0% height at the root end and 100% height atthe tip end, and wherein the last stage bucket is twisted in a sectionbetween 30-60% height to a degree that is higher than other sections ofthe bucket.
 13. A turbine according to claim 9, wherein the last stagebucket is twisted at the root end to a degree that is higher than othersections of the bucket.
 14. A turbine according to claim 9, wherein atan operating speed of 3,600 RPMs, a maximum height of the last stagebucket is 35 inches.
 15. A turbine according to claim 9, wherein at anoperating speed of X RPMs, a maximum height of the last stage bucket is3600/X*35.
 16. A method of reducing flow induced vibration in a laststage turbine bucket, the turbine bucket being twisted from a root endto a tip end, the method comprising twisting the turbine bucket to adegree that defines an accumulated angular offset of the tip end in arange of 10-15° relative to a tangential direction, thereby reducingexcess negative incidence by 15-20° relative to the tangentialdirection.
 17. A method according to claim 16, wherein the twisting stepis practiced such that the degree of twist defines an accumulatedangular offset of the tip end of 13°, thereby reducing excess negativeincidence by 17°.
 18. A method according to claim 16, comprisingradiusing a leading edge of the turbine bucket to reduce positiveincidence performance sensitivity.